Hello Mike,
Thanks for joining the site. I so far haven't tried anything other than pulling weeds. I have heard that Dymondia can be effected by some weed killers though. I would suggest that you try a very small spot if you start going the chemical route. So far, my established Dymondia has pretty much squeezed out all but the occasional weeds, but I have no clover around here and it sounds like I should count my blessings.
Please let us know if you do some trials, there are a lot of people that would be glad to learn from your experience.
I would love to see some photo's of your lawn and add them to the
Dymondia Gallery